Cydney is proving that perpendicular lines have slopes that are opposite reciprocals. She draws line p and labels two points on the line as (0, a) and (b, 0). Enter the answers, in simplest form, in the boxes to complete the proof. The slope of line p is . Rotate line p 90° counterclockwise about the origin to get line q. The labeled points on line p map to (−a, 0) and ( , ) on line q. The slope of line q is . The slopes of the lines are opposite reciprocals because the product of the slopes is .

Slope of p  =    -a/b

(0, b)  is on line  q

Slope of q  =  ( b - 0) / (0 - -a)  =   b/a

Product of the slopes  =  (-a/b) (b/a)  =  (-ab) /(ab)  =  -1

I hope this helps (: Have a whimsical day! lol

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations: